Use of global positioning satellite (GPS) receivers in automotive navigation, emergency messaging, and tracking systems is now widespread. However, systems based solely on GPS generally do not work well in dense city environments, where signal blockage and reflection by tall buildings, in addition to radio frequency interference, often occurs. A cost effective solution to this problem is to augment the GPS receiver with some form of Dead Reckoning (DR), to fill in the gaps occurring as a result of loss of GPS coverage and improve the accuracy of the GPS trajectory.
A DR system may take the form of an interface to separate left and right wheel sensors installed in the vehicle to provide an indication of the speed of each wheel. The average speed of each wheel is used to determine the vehicle velocity, while the wheel speed difference divided by the distance between the wheels (the wheel track) is used to determine changes in the vehicle heading. The accuracy of the DR system is critically dependent upon the accuracy to which the vehicle's heading is determined whereby each degree of heading error, in the absence of GPS, produces a cross-track position error which grows approximately as 1.7% of distance traveled.
A substantial source of error in the use of differential wheel speed to track the heading of a movable vehicle is the difference in the sizes of the two tires on which the speed sensors are installed. This differential tire size, if unknown to the navigation system, produces an error growth in the predicted heading of the vehicle which grows linearly with distance traveled, and a cross-track position error which grows quadratically with distance traveled. Even a minute difference in tire size can produce very large navigation error: a ratio in tire sizes of 1.001 (corresponding to one tire being 0.1% larger then the other) will produce 300 meters of cross track position error after only 1 kilometer of travel.
U.S. Pat. No. 5,402,365, assigned to the same assignee of the subject application, describes a system for estimating the differential scale factor but requires periods of essentially straight travel to perform an adequate calibration and does so without the use of GPS. Such a system may degrade in accuracy and/or speed of convergence in areas where straight roads are the exception (e.g., as exists in Europe).
Accordingly, the present invention reduces this error growth by automatically calibrating the differential scale factor (i.e., the ratio of the tire sizes) between the left and right wheels by utilizing GPS information and a Kalman filtering algorithm thereby exhibiting rapid and accurate calibration, independent of road turns or shape.